Club for Growth president Chris Chocola agreed the next round of talks puts the GOP in a better negotiating position. The "fiscal cliff" debate, he said, "wasn't a clean scenario with current law and rates going up, so people can argue with themselves and say, 'If I had done nothing, it'd be worse.' The debt ceiling doesn't have that application. It's pretty simple."

Republicans this time around, Chocola said, should have "a simple message, a sympathetic public and all the leverage in the world if they're willing to use it." That said, he added, "I'm never optimistic about congress doing the hard things."

Mr. Obama has made it abundantly clear that he doesn't think it's appropriate for Republicans to use the debt limit as a bargaining chip and thus threaten to let the nation default on its debt. "I will not have another debate with this Congress about whether they should pay the bills that they've already racked up through the laws that they passed," he said Tuesday night. "We can't not pay bills that we've already incurred."

Conservatives like Inhofe and Johnson, however, aren't afraid to use the debt limit as leverage. "In another month from now, all these tea party people and others are going to be together and using that as the hammer to get that done, and I feel very good about that," Inhofe said.